Monte Carlo (MC) linear solvers can be considered stochastic realizations of deterministic stationary iterative processes. That is, they estimate the result of a stationary iterative technique for solving linear systems. There are typically two sources of errors: (i) those from the underlying...

Water management, in a variety of contexts and objectives, is a very important issue gaining increasing attention worldwide. In some places and during some periods, this is due to the scarcity of the water resource, and increasing competition for its use. In some others, it can be risk reduction...

This paper considers the passage of a parallel, uniform stream of particles through a parallel-sided, homogeneous slab of material capable of scattering and absorption. Particle histories are followed until the particle escapes from the near or far surface of the slab. Each particle carries a...

Algorithms for estimating the integral over hyper-rectangular regions are discussed. Solving this problem in high dimensions is usually considered a domain of Monte Carlo and quasi-Monte Carlo methods, because their power degrades little with increasing dimension. These algorithms are compared...

It is well known that there is no analytic expression for the electrical capacitance of the unit cube. However, there are several Monte Carlo methods that have been used to numerically estimate this capacitance to high accuracy. These include a Brownian dynamics algorithm [H.-X. Zhou, A. Szabo,...

In this paper, we propose an estimator for pricing high-dimensional American-style options and show that asymptotically its upper bias converges to zero. An advantage of the proposed estimator is that when combined with low discrepancy sequences, it exhibits a superior rate of convergence....